If perk is enabled starting Forrest Warrior Chainsaw clips through character's backpacks, e.g. Arnetta and Bunko characters.
This is resolved when you pick-up Forrest Warrior Chainsaw on the map.

Subsequent Forrest Warrior Chainsaw pick-ups on the map are not improved by the perk.
Starting chainsaw has 150% damage and 150% fuel.
Those picked-up on the map have 100% fuel and probably 100% damage.